NASA Technical Reports Server (NTRS) 20020032743: Effects of Aircraft Wake Dynamics on Measured and Simulated NO(x) and HO(x) Wake Chemistry. Appendix B

15 Pages·1.1 MB·English

by  NASA Technical Reports Server (NTRS)

APPENDIX B
Effects of Aircraft Wake Dynamics on Measured and Simulated
NOx and HOx Wake Chemistry
D.C. Lewellen and W. S. Lewellen
Journal of Geophysical Research
Vol. 106, No. D2 l, pages 27,661-27,672
16 November 2001
12
Effects of aircraft wake dynamics on measured and
simulated NO_ and HO_ wake chemistry
D. C. Lewe]len and W. S. Lewellen
Department of Mev_haaical and Aerospace Engin_ring, West Virginia University, Morgantown,
West Virginia, USA
Abstract. High-resolution numerical large-eddy simulations of the near
wake of a B757 including simplified NO_ and HOz chemistry were performed
to explore the effects of dynamics on chemistry in wakens of ages from a
few seconds to several minutes. Dilution plays an important basic role in
the NO_ - Oa chemistry in the wake, while a more interesting interaction
between the chemistry and dynamics occurs for the HO_ species. These
simulation results are compared with published measurements of OH and
HO2 within a B757 wake under cruise conditions in tile upper troposphere
taken during the Subsonic Aircraft Contrail and Cloud Effects Special Study
(SUCCESS} mission in May 1996. The simulation provides a much finer
grained representation of the chemistry and dynamics of the early wake
than is possible from the 1 s data samples taken in situ. The comparison
suggests that the previously reported discrepancy of up to a factor of 20 -
50 between the SUCCESS measurements of the [HO2]/[OH] ratio and that
predicted by simplified theoretical computations is due to the combined
effects of large mixing rates around the wake plume edges and averaging over
volumes containing large species fluctuations. The results demonstrate the
feasibility of using three-dimensional unsteady large-eddy simulations with
coupled chemistry to study such phenomena.
1. Introduction
measurements, is an important source of uncertainty in
interpreting the results of such field measurements or
The possibility that future, increases in the commer- results from atmospheric chemistry models. When the
cial aircraft fleet may have significant environmental sampling volumes being measured (or modeled) con-
and climatological effects is being widely studied [e.g., rain large fluctuations of some chemical species, the av-
Penner et. al., 1999; Schumann, 1998: Friedl, 1997]. e.rage concentration measured and chemistry inferred
While the volume of aircraft emissions is not large com- may be quite different from the locM results occurring
pared to ground-based sources, these emissions are in- within that volume. This is particularly true when re-
jected directly into the relatively stable upper tropo- action rates between relevant species are faster than
sphere and lower stratosphere where small emissions turbulent mixing rates, allowing strong anticorrelated
may have potentially significant effects. A number of distributions to occur. This necessarily reduces the ef-
field programs have been conducted, e.g., Subsonic Air- fective reaction rate of average concentrations, making
craft Contrail and Cloud Effects Special Study (SUC- those rates dependent on mixing rates in the fluid [Sykes
CESS) [Teen and Miake-Lye, 1998], SASS Ozone and eta/., 1992; Schumann, 1989].
Nitrogen Oxide Experiment (SONEX) [Sinffh et al., Here our focus is on the dynamics and chemistry
1999], and AERONOX [Schumann, 1997], which use in
within a wake plume from an age of a few seconds to
situ measurements in wakes as a means to better deter-
several minutes. This is a regime which has been heavily
mine the aircraft emi_ions and understand the chemi-
studied in in situ measurement campaigns. It includes
cal kinetics within the wake plume. Our subject in this the partial capturing of the exhatmts by the tr',dIing
work, the effects of wake dynamics on wake _emistry
LEWELLEN AND LEWELLEN
vortexpairbehindtheaircraft,thevortex-dominatedclude studies of detailed chemistry, in the early hot jet
dynamicwshichd_axila_,iceaxllpyandthewakeplume regime coupled with simple dynamics [e.g., Miake-Lye
bothverticallyandhorizontallya,ndthesubsequentet al., 1993; Menon and Wu, 1998; KSrcher et al., 1998];
buoyanct_scillations of the plume after the vortex dy- studies with detailed chemistry in the wake vortex
namics subside. We do not consider the chem£stry in regime with dynamics modeled in two dimensions [e.g.,
the earliest jet exhaust phase where temperatures are Anderson et al., 1996}; studies of older plumes with de-
initially very high but rapidly dilute toward ambient tailed box model chemistry but only rudimentary dy-
levels, or the ultimate fate of the wake plume and its namics included via some prescribed dilution history
chemical constituents at late times where the dynamics [e.g., Karol et al., 1997]; studies with detailed 3-D air-
are dominated by ambient atmospheric turbulence, al- craft wake dynamics but only passive tracers for the en-
though both are likely to prove important in assessing gine exhausts [e.g., Lewellen and Lewellen, 1996; Gerz
the environmental effects of aviation. and Ehret, 1996; Gerz et al., 1998; Lewellen et al., 1998];
and studies of ice phase "chemistry" (contrails) inter-
During this time period we are particularly inter-
acting with wake dynamics at many different levels of
ested in the impact of species fluctuations on scales that
approximation [e.g., Gierens, 1996; Chlond, 1998; Suss-
are typically too small to be measured by trailing air-
mann and Gierens, 1999; Gierens and Jensen, 1999;
craft moving at speeds often in excess of 200 m s kl.
Lewellen and Lewel_en, 2001; Sussmann and Gierens,
Accordingly, we utilize a three-dimensional (3-D), un-
2001]. Aircraft wake dynamics alone, ignoring the fate
steady, high-resolution model of the aircraft wake which
of the engine exhaust products, have also been a sig-
is capable of resolving dynamical and/or chemical fea-
nificant area for research because of potential effects on
tures on scales of a few meters. The large-eddy simu-
closely following aircraft and the resulting safety issues
lation (LES) code we. employ for the fluid dynamics is
for takeoff and landing at airports. A recent review of
the same one used by Lewellen and LeweUen [1996] to
these efforts, including some large eddy and direct nu-
present detailed dynamics of the vortex pair breakup in
mericai simulations, has been made by Spalart [1998].
an aircraft wake; by Lewellen et al. [1998} to compare
numerical simulation results of wake dispersion to lidar In s_.tion 2 we provide an overview of our LES model
observations; and by LewelIen and Lewellen [2001] to and the conditions simulated. In section 3, we discuss
examine effects of wake dynamics on contrail evolution. the simulation results, beginning with the basic wake
Given the computational requirements of the resolution dynamics and NO_ - ozone chemistry, as illustrated by
we employ, we can include only a limited set of chemical the simulations, and ending with the dramatic effects of
reactions and species within our simulations. Nonethe- dynamics on measured H()_ chemistry in the wake. A
less, this proves sufficient to demonstrate some poten- summary and some final comments follow in section 4.
tially important effects, while confirming the practical
feasibility of coupling detailed dynamics and chemistry
2. Model Overview and Simulation
using LES.
Conditions
Of particular interest to us in this study were a set of
HO,. measurements taken during SUCCESS {Tan el al.. In order to simulate detailed wake dynamics, species
1998]. These showed an apparently anomalously high
dispersion, _md the accompanying chemistry, we use
ratio of [ttO2]/[OH] within young wake phlmes, 20 5{) the technique of numerical large-eddy simulation. The
times greater than expected by simple chemical compu-
r,'mge of length scales involved in this problem is much
tations. The authors suggested that this effect might
too great to permit a direct numericaJ simu]ation of all
be due in part to the _rong ;mticorrelation betwee, n
scales with currently available computer resources. In-
NO and HO2 in the turbulent fluctuations within the
stead, we solve the Navier-Stokes equations directly for
wake occurring during these measurements. To quan-
the most important scales in the flow (from smaller than
titatively test this possibility, we have included HO_ the wake vortex core size to many times the aircraft
chemistry in addition to basic NO_ - ozone chemistry
wingspan), but only model the etfects of the smaller, un-
in our reaction set for the present work, and have cho-
resolved eddies. Our simulation is of a B757 flying in the
sen to simulate a B757 wake with nominal conditions
upper troposphere under cruise conditions, nominally
and emissions in agreement with those reported during that relevant for the SUCCESS observations. Details
the SUCCESS HO_ mea.surements.
of our LES model applied to aircraft wake dynamics
Our approach here is complementary to other recent have been given by LeweUen and Lewellen [1996, 2001],
studies of chemistry in aircraft wake plumes. These in- along with a discussion of the many choices and corn-
AIRCRAFT WAKE DYNAMICS AND CHEMLSTRY 3
promises necessarily involved in efficiently tackling such perature gradient or a stable rotational velocity field
simulations. A summary of the model and simulation is approximately included via appropriate reductions of
conditions is given below, first for the fluid dynamics the subgrid turbulence length scale. The incorporation
and then for the chemistry added specifically for the of rotational damping effects in the subgrid model is
present work. ,somewhat unusual, but u,_ful for simulations of _rong
vortices in order to avoid unphysically large rates of core
2.1. Fluid Mechanics diffusion. The method is described in detail by Lewellen
et al. [2000], who used it extensively in tornado simula-
The LES code we employ for aircraft wake simula-
tions. It was not included in our earliest aircraft wake
tions is a modified version of one we use for bound-
simulations [Lewellen and Lewellen, 1996], but has been
ary layer cloud modeling [e.g., Lewellen and LeweUen,
used since [Lewellen et al., 1998; Lewellen and Lewellen,
1996], which in turn is based on the implementation of
20011.
Sykes and Henn [1989]. It is a 3-D finite difference im-
We employ periodic boundary, conditions in all three
plementation of the incompressible Navier-Stokes equa-
directions. Effectively, this means there are neighboring
tions in the Boussinesq approximation, second-order
wakes Located at twice the distance to the boundary in
acc_ate in space, and time. It incorporates a piecewise
parabolic model algorithm for the advection of thermal the vertical and crosswise directions evolving in parallel
with our simulated wake. The stretched grid allows us
energy and species concentrations. The pressure field
to place the boundaries at sufficient distance to make
is obtained by directly solving the Poisson equation us-
ing fast Fourier transforms in the downstream direction, the effects of these image vortices negligible. Period-
icity in the vertical is modified by a temperature shift
the method of Farnell [19801 for nonuniform grids in the
between the top and bottom of the domain to permit a
cross-stream direction, and a tridiagonal solver in the
vertical. mean stratification to be imposed. In imposing periodic
conditions in the downstream direction we are treating
The simulation of the interacting trailing vortex pair
the wake portion within our domain as if it were laid
in an aircraft wake presents a particular challenge be-
down instantaneously. This ks an appropriate approxi-
cause both small grid spacings and large domains are re-
mation here because the aircraft flight speed is much
quired. A grid spacing of a few percent of the wingspan
greater than the velocity scales of the wake dynam-
or less is required to resolve the trailing vortex cores
ics over the period treated (which excludes the region
and the transport of the engine exhausts around and
within a few wingspans of the aircraft.). The approxi-
into them. At the same time, line vortices have a sizable
mate periodicity of the wake downstream is amply con-
long-range influence on the flow field, so domain widths
firmed by observations of contrail evolution from ages
of several wingspans or more are required to minimize
of a few seconds to several minutes.
unwanted boundary interactions. We employ three, de-
The initial conditions were chosen consistent with
vices to help to meet these conflicting demands: (1) a
cruise conditions for a B757 flying at 11 km altitude at
stretched grid spacing in the vertical and cross-stream
210 m s t with a mass of 87,000 kg (which is midway
directions to achieve fine spacing where it is m_ded
between the minimum and maximum masses for this
within the wake. while maintaining large domain sizes;
aircraft). For an effective vortex pair separation of 29.4
(2) vertical tracking of the wake to insure that the fine
m this implies a circulation about the vortices of 380
grid portion of the domain encompasses the descending
m2 s 1. The heat produced by the engines per meter
wake vortices; and {3) different grids (six in the case
of flight path was taken as 255 K m2, computed from a
presented here) for different segments of the simulations
total fuel flow ra_e of 3.1 kg krn -1 (in agre, ement with
as the wake evolves and the optimum grid requirements
that quoted for the SUCCESS measurements by Tan
change. A variable time step was used in the simula-
et aL [1998]), a specific combustion heat of 43 MJ kg t
tion, with values ranging from 0.003 to t}.02 to 1 s for,
appropriate for kerosene-type jet fuels, ;rod an assumed
respectively, the early jet, early vortex, ;rod bate time
jet engine efficiency of 30%. Tbe integrated momentum
stages discus_d below.
in the exhaust jets per meter of flight path was chosen
We errlpIoy a subgrid moctel which u._es a quasi-
_Ls502 m3 s t, computed from the as,sumed fuel flow
equilibrium, second-order turbulence closure scheme
rate, flight speed, and a specific fuel consumption of
with the suhgrid turbulent kinetic energy carried as a
16.9 mg N-j s-1. The detailed cross-stream distribu-
dynamical variable and the maximum subgrid turbu-
tions of the velocity fields and exhaust products depend
lence length scale related to the numeric',d grid length.
on the roll up of the vorticity shed from the wing and
The damping of subgrid turbulence by a stable tern-
LEWELLEN AND LEWELLEN
were taken from a UNIWAKE simulation [Quackenbush mize boundary effects and allow a more realistic ambi-
eta/., 1996], with values scaled so as to match the de- ent turbulence field. There is a different constraint on
sired circulation, jet momentum, engine heat, etc. the downstream domain size as discussed at length by
As we will discuss in detail below, the fluctuations in Lewellen and Lewellen [1996]. The downstream domain
size. mnst be commensurate with the period of the basic
exhaust distribution play an important role in affecting
wake decay mode, the Crow instability (discussed be-
measured chemistry in the wake. Accordingly, we have
at least approximately included the effects of exhaust low). For a given aircraft, there is considerable variabil-
jet turbulence into the initial conditions used for our ity in the observed periodicity, depending on the wave
chemistry simulation. This was done by performing an and turbulence spectrum in the ambient atmosphere. It
initial simulation of the early wake (without chemistry) is not unusual to see a factor of 2 variation in period
from an age of about 0.5 s to 3.5 s, with high spatial within a single contrail in the sky. Nonetheless, there
resolution (0.33 m finest grid spacing), for a short (42 is a preferred range of wavelengths encountered. Here
we choose a downstream domain dimension of 210 m,
m) downstream portion of wake, to develop some jet
turbulence and smaller-scale fluctuations in the exhaust expecting a Crow period of approximately that length,
which for the B757 is a little less than the wavelength of
distribution. These results were periodically continued
to provide the initial conditions for the full downstream maximum amphfication deduced by Crow [1970] from
a linear stability analysis, and a little greater than the
domain employed for the chemistry, simulation.
most favored range found in the direct numerical sim-
To complete the initial conditions for our simu-
ulation study of Spalart and Wray [1996]. In previous
lations, the aircraft wake is superimposed with an
work we have found little variation of the basic wake
ambient atmospheric field (the result of a separate
decay (rate of wake dispersion, overall vertical and hor-
large-eddy simulation), as described by LeweUen and
izontal extent, wake lifetime, etc.) with downstream
Lewellen [1996]. The field was generated in the desired
domain size. The intcraction between a given Crow pe-
domain, with a nominal value of potential temperature
riod and its neighbors is only weakly affected by the
stratification for the upper troposphere (2.5 K km -1)
detailed structure of those neighbors, so replacing them
and no mean wind shear. Large initial velocity and
with periodic images proves to be a reasonable approx-
temperature perturbations were applied and the subse-
imation. Providing for multiple Crow periods to be
quent evolution followed via LES until the turbulence
simulated does give additional turbulent realizations of
and gravity waves had a chance to adjust to the stratifi-
these structures. We performed an additional simula-
cation, and their amplitude had decayed into a reason-
tion analogous to the one presented here but with a dif-
able range (turbulent dissipation rate of order 2 x 10-'_
ferent ambient turbulence field (with lower turbulence
In 2s- 3).
intensity) to estimate the variation in our chemistry
Table 1 summarizes the grids employed for the pri- results between different turbulent realizations of the
mary simulation. The choice of grid for the given seg- same basic process. For the summary results presented
ment of the simulation was correlated with the wake
below, the two sets of results were all very close.
vortex dynamics then occurring, in order to be_t appor-
tion the limited number of grid points available given
2.2. Chemistry
the physics that had to bc res_)lved. As the dynam-
ics progress the wake expands mid turbulence levels Given the number of grid points in our simulations,
fall. so that the finest grid spacing can he increased on we use a relatively simple (and therefore numerically
subsequent grids but must cover larger portions of the less costly) chemical reaction set, concentrating on im-
domain. Accordingly, when the wake dynaznics would portant reactions within the wake plume for ages from
threaten to outgrow the fin_grid region of the domain, a few seconds to a h_w minutes. The chemical species
we simply interpolated the species and flow fields to a considered are NO, NO..,, HONO, HNO3, 03, OH, HO2,
more suitable grid. The domain size was doubled for CO, and CIt4, with bmsie reactions:
the fourth grid. To do this, the final field generated
on the third grid was periodically doubled in the down- NO + O,_ ---+ NO2 + 0..,, (1)
stream direction and added to an _unbient turbulence
NO2+h.+()_ ----+ NO+O,3, (2)
field generated by a separate LES on the doubled do-
HONO+h. ---+ OH+NO, (3)
main.
As noted prcviously, the vertical and cross-stream Oil + NO ---+ IIONO, (4)
domain edges were chc_sen far from the wake to mini- OH+NO._ ---+ HNOa, (5)
AIRCRAFT WAKE DYNAMICS AND CHEMISTRY
Table 1. Grids Used for the B757 Chemistry Simulation _
Grid Domain, m Number of Grid Points Fine Spacing, m Time period, s
0 660x660x42 162x154x130 0.33x0.33x0.33 0.5-3.5
1 660x800x210 124xl16x130 0.8x0.Sxl.6 3.5-50.
2 660x800x210 120x121x162 1.xl.xl.3 50-100
3 660x900x210 152x134x130 1.6xl.6xl.6 100-240
4 1200x1300x420 100xt39x122 3.3x3.3x3.5 240-500
5 1200x1300x420 94xl19x66 6.5x6.5x6.5 500-900
_Domain dimensions, number of grid points, and fine grid spacings are given for the (cross-
stream)x (vertical)x(downstream) directions, respectively. Grid 0 was used for an initial simula-
Lion without chemistry to generate initial conditions including turbulent jet fluctuations for the
main simulation.
H02 + NO ---+ OI-I + NOz, (6) during the SUCCESS flights: ambient background lev-
OH + CO + 0.2 ----+ CO2 + tlO.2, (7) els of HO2 between 10-20 pptv and OH between 0.3-0.5
pptv [Tan et al., 1998]; ambient levels of NO_ = 70
OH + 0:, ---+ ttO.2 + 02, (8)
pptv, CO = 120 ppbv, O3 = 65 ppbv, and CH4 = 1750
HO2 + ()._ ---+ OH +202, (9) ppbv [Jaegle et al., 1998]. The actual values used for
OH+CH4+... ----4 HO2+N02+ .... (10) the HONO, OH, and H02 concentrations (HONO =
0.36 pptv, OH = 0.42 pptv, and HO2 -- 15 pptv) and
the split of NOz into NO and NO2 (NO = 55 pptv and
The reaction rates employed (k_-o+o3 = 2.39x 10-5,
NO2 = 15 pptv), were also chosen so that the back-
kOH+NO = 4.63X10 -2 , kOH+NO2 = 9.18X10 -2 ,
ground concentrations of any species did not drift sig-
/¢HO_+NO = 8.4X10 -2, kOH+CO = 1-29x10 -:_, koH+Oa
nificantly over the course of the simulation (realizing
= 1.59x10 4 kuo2+o_ = 8.32×10 -s, ko}_+CH4 =
that other reactions besides those explidtly treated are
5.2x10 -_, 'all in (ppb s)-l) were taken from DeMote
important in setting the background equilibrium con-
et al. [1997] for conditions of 217 K and 0.224 arm, ex-
centration over timescal_ much longer than we consider
cept for the OH + NO2 re_ction rate, which was taken
here).
from Brown et al. (1999]. Nominal daytime values at 11
The initial concentration used for each species con-
km altitude were chosen for the photolysis rates (JNo_
sisted of a background level plus a plume concentration,
= 0.01 s-1 and J_oNo = 0.0033 s-l). Reaction (10) is
with the latter chosen consistent with measured emis-
an effective one for the cycling of OH to HO2 through
sion indices, fuel consumption rates, and flight speeds
the intermediary CI1.tO2 in the presence of NO. It is
f_w the SUCCESS flights. In particular, the NO emis-
only of minor importance to the HOz chemistry in the
sion index is taken a,s 7.,5 g NO2 kg -l fllel [Campos
regime being studied (being dominated by reaction (7)),
et al., 1998], with a total fuel usage per flight path of
but is included approximately at little extra numerical
3.1 g m-l. The volume ratio of CO above background
cost by taking the CH4 concentration as constant. The
in the exhaust to NO_ was set at 0.306, consistent with
variations of the rate constants due to temperature fluc-
the median emission index (1.55 g kg 1) measured on
tuations within the wake plume have not been included
May 4 during SUCCESS [Vay et aL, 1998]. The ratios
here. For the wake ages considered, the variations in
of HONO and NO2 to NO, in the jet are set at nominal
temperature encountered are generally of order a de-
values of 0.04 and 0.1, respectively. The initial plume
gree or less, giving changes in rate constants of a few
e×ce_(_ over background for HN():_, O:_, CH4, OH, and
percent or less (which is generally below the level of
H()2 were taken to be zero.
uncertainty in the rate formulas them_lves).
In choosing the initial chemical concentrations, we The biggest numerical costs of including chemical re-
actions within our LES axe the "added memory required
did not try to match a particular SUCCESS flight con-
for the 3-D species fields and the added computation
dition, but did pick values within the ranges measured
LEWELLEN AND LEWELLEN
involved in advecting and diffusing them as governed 3.1. Review of Basic Wake Decay Mode and
by the flow field. Accordingly, it is useful to minimize Species Dispersion
the number of species which must be carried as dy-
Figure 1 illustrates some of the simulated wake dy-
namical variables. We reduce, this number by two by
namics ou_ to an age of 10 rain, as visualized by the
idezatifying three, combinations which are.con,_rved by
cross-stream integrated NOz distribution in the wake
equations (1)-(10) (so that their plume concentrations
plume. Since NO_ is es_ntially a conserved species, the
above background always remain proportional to each
distribution shown is a result of dispersion only. The
other): NO + NO2 - OH - H02 (essentially NOz within
format is as described by Lewellen et al. [1998], inspired
the plume); H02 + OH + HONO + HNOa (which we
by scanning lidar measurements of wakes. The wake is
use after the computation to solve for HNO3); and CO
sampled as if it were being advected at a steady rate
(which is conserved to a high degree of accuracy because
by a mean wind aligned with the wake. The horizontal
the CO levelseverywhere areso much greaterthan the
axis then varies over time and downstream distance so
OH levelswhich erode itvia (7)).
that both the temporal evolution and spatial structure
In numerically implementing (1)-(10),one point re-
c_a be see_n. The "drift velocity" determining the unit
quiresparticularcare. Some of the reactions involv-
of distance per unit of time has been chosen to be 9.5 m
ingOH and HO.2 (equations (4)-(6)) proceed on a very.
s-I , which is in a convenient range for displaying both
short timescale within the core of the wake plume where
the temporal and spatial structure. In the figure the
the NO_ concentrations are high, shorter than the time
vertical distance scale has been expanded by a factor of
step required to accurately follow the flow dynamics.
3 relative to the downstream distance scale for clarity.
We cannot simply use equilibrium values for OH and
The main features of the wake evolution can be fol-
H02 because the timescale for the relevant reactions
lowed in this figure. We give only a brief summary of
does not remain small (compared to the time step ap-
the dynamics here; more detail may be found in our pre-
propriate for the flow dynamics) within the edges of
vious papers. The early wake dynamics are dominated
the plume. Instead, we update the OIt and HO2 chem-
by the vortex pair which results from the lift gener-
istry semi-implicitly. In short domain tests we have con-
ated by the aircraft's wings. For the first minute or so
firmed that the simulated OIt and [IO2 concentrations
the vortex pair descends rapidly. Initia/iy, the engine
evolve correctly in time within the plume edges, while
exhaust distribution is stretched and advected by the
giving the correct equilibrium values within the plume
velocity field accompanying the vortex pair, giving a pe-
core, regardless of the time step chosen. The remaining
riod of very rapid dilution. Subsequently, the exhausts
reactions progress on timescales which are comparable
axe partitioned into three, different populations: rela-
to or slower than the flow timc_cales; consequently, the
tively high concentrations in and immediately around
chemistry for the species other than OH and HO.2 are
the vortex cores where mixing rates are low; midievel
updated explicitly in time.
concentrations and mixing rates within the ellipse of
fluid surrounding and descending with the vortex pair;
and lower concentrations and higher mixing rates within
a fraction of the exhausts which is not ultimately en-
trained into the falling vortex system (or becomes de-
trained from i_) and remains c|ose tt) tlight level. The
3. Results
fraction of exhausts finding its way into each population
is most strongly influenced by the engine placement of
The chief impact of wake d)mamics on the chemistry the particular aircraft, but is also influenced to a lesser
is through plume mixing. This reduces concentrations extent by the atmospheric turbulence levels, shear, and
stratification.
of exhaust constituents, mixes fresh ambient air with
plume air, and produces tluctuations in plume distribu- While the vortices descend, perturbations of the vor-
tions. It is appropriate, then, in explaining the simula- tices from the ambient atmosphere (and/or unsteady
tion results, that we begin with a summary of a typi- wing loading or jet turbulence) grow via the Crow in-
ca] wake decay history m,d its etfects on passive plume stability [Crow, 1970] . The rate of growth depends
dispersal. Simple NO_ 03 chemistry is considered primarily on the wavelength of the perturbation, the
next before turning to tlOr chemistry, where we find vortex spacing, and circulation. In a turbulent atmo-
the most interesting effects of dynamics on chemistry sphere the w)rtices see a superposition of perturbations,
illustrated by our simulations. and the instabilities for different wavelengths compete
A_[RCRAFT WAKE DYNAMICS AND CHEMISTRY
15B. n n i I I
IIl_]tlllllllll$l;IJ1Jl
-,s, l
-31111.
-45o, i i J i I i I I i I 1 i I L _ I i L I I i I I i I i _ i I
O. 1El0. 2an. _, 4.. so°. 6QB.
time (s), distance (m * 9.5)
[ ,;_
0 5O 1.0 1.5
Figttre 1. Downstream space/time versus height plot of cross-stream integrated plume NO= (in ppm m) for a
simulated B757 wake.
with each other. Those which are in the range of most we find that this oscillation drives the dominant turbu-
rapid growth and have the largest initial perturbations lence that mixes the wake. plume until it damps, after
eventually win out. 1-3 Brunt-V_dsSdg periods, to the level of the ambient
The growth of the Crow instability proceeds until the atmospheric turbulence. The Brunt-V_iis_i oscillation
vortices touch, reconnect, and form elongated vortex can be seen in the long-timescale (10 min period) ver-
rings. This occurs at a wake age of around 80 s in the tical modulation evident in Figure 1.
present B757 simulation. During the reconnection pro- There are variations in the details of this basic wake
cess some of the exhausts escape from the vortex system decay mode depending on aircraft and atmospheric con-
and buoyantly rise. The distribution of the remainder ditions, but that illustrated is typical. We have found in
is significantly scrambled so that the peak concentra- simulations of wakes and observations of contrails that
tions no longer provide a clear signature of the vortex the dynamics of the Crow instability primarily govern
dynamics. The vortex rings continue to descend and, at the wake decay for a wide range of conditions in the
the same time, open up in the cross-stream direction, absence of large wind shear.
thereby significantly increasing both the vertical and
horizontal extents of the wake. They can further inter- 3.2. NO= - Ozone Chemistry
act with themselves, even sometimes relinking again to
form two rings from one. This, together with the contin- Figures 2-4 summarize the evolution of several chem-
ual diffusion of the vortex core_s (due to the smaller-sc_aJe ical species during the wake decay. All of the concen-
atmc_spheric turbulence and interaction with the ambi- trations plotted are excesses above (or below) the con-
ent stratification), eventually leads to the demise of the stant background level. Consider first the evolution of
orgartized vortex system. In the present simulation the the NO, N02, and ]IONO concentrations. These are
descent of the vortex rings (or their remnasats) continues dominated by plume dispersion. The local peak con-
until an age of approximately 230 s, with about half of centrations of these species fall sharply (Figure 2) for
the total wake descent (of _320 m) occurring after the the first _25 s as the jet exhausts mix throughout the el-
pair initially relinks. It is the descending vort,cx rings lipse of fluid falling with the vortex pair. Subsequently,
which (for appropriate ambient humidity) give rise to they fall nearly linearly while the vortex-driven turbu-
the periodic series of puffs often se.e.n in contrails. lence dominates and more slowly when the vortex sys-
tem dissolves and the weaker Brunt-V'Xis:fil_i sloshings
The coherent wake dynamics do not end with the
take over. There is a notice_able enhancement in the di-
dissolution of the wake vo_ices. The positive buoy-
lution rate of the peak concentrations for a period after
ancy acquired by the vortex system's d(_cent through
vortex linking occurs, with its accompan_ng scrambling
the stratified atmosphere (together with the heat in the
of the exhausts. The peak local concentrations are lo-
initial engine exhaust) drives a strong Brunt-V_s/il/i
cated within the lowe.st (vortex-dominated) part of the
oscillation. In the absence of signiticant wind shear,
wake plume until about the 250 s point, after which the
8 LEWELLEN AND LEWELLEN
_.0
E
t
!
[_o.o'_-\ ................ -.
==
t_--_.\ "--.
7,
¢)
_o
\__
g.
10-= -[Ho,] / 4a
[o_l I
.5
10-a .... , , , ,,L I, ,,
10' 1# 10=
ume (.)
time (s)
Figure 2. Peak concentrations of chemical species in Figure 4. Integrated wake plume concentratiorr_ above
the wake relative to background versus time. background per meter of flight path versus time.
.... i ........ i
look more like that in Figure 3 (corresponding to 1 s
1#
saznples of a chase aircraft maintaining a constant .sep-
aration behind the lead aircraft). The NO, NO_, and
HONO concentration histories in Figure 3are well cor-
related with those in Figure 2,but with some noticeable
differences• The downstream average peak concentra-
tions drop much more steeply between about 50 and
100 s as the vortices are twisted by the growing Crow
.a _-.- -[o._J --... ---. _ instability. The peak measured concentrations remain
___ -- ,,_-_._,.__ -_. located with the vortices during this period, but sub-
_10-'
"_\ "_--.._ seque.ntly shift to the exhausts released by the vortex
_" _---I-[NO ] \ "--'-
Z j......-.'_ ",_ _.___. _- system during the linking process. These buoyantly rise
to rejoin the upper wake at about 18(1s.
10-=
_....-----'____ -[HOJ _"-_T_-
The plume-integrated amounts of NO, NOu, and
-- lo.l ............. _ ..... -._
ItONO vary. much more slowly, in response to the wake
10-= "-_ '-.._..,.,_ ('hemistry itself (Figure 4). The plume NO isslowly con-
10' 1Es 10= verted to NO_ via (1); the initial ratio of [NO_]/[NO]
Ume (,)
= 0.11 will eventually rise to approarh its background
Figure 3. Peak down.ream averaged wake plume con- equilibrium value for the present conditions of 0.27 as
centrations relative to background versus time. the plume dilutes. The total HONO is slowly depleted
via photolysis, with a corresponding nearly linear rise
in HNOa to approximately 2.6% of the plume NO_ at
900 s. The time evolution of the peak HNOa concentra-
peak is located near the original flight level, within the
upper wake (which, beinl_ less turbulent, dilutes at a tion (FigaEe 2) represents a competition between this
slower rate). production and the plume dilution.
In an in situ measurement, a following aircraft ob- The OH and HO2 behavior in the plume are quali-
tains not a strictly local concentration, but the average tatively different. As we will discuss in more detail be-
over some finite sampling vohlme. A corresponding plot low, the differences from background for these species
of peak mea.sured concentration versus plume age would axe more nearly constant within the plume, so that the
AIRCRAFT WAKE DYNAMICS AND CHEMISTRY
integrated contribution scales approximately with the the sources and sinks of OH and H02 are slow compared
plume volume. There is a sharp initia! increase associ- to the exchange reactions between them, so that the
ated with the early mixing of the exhaust jets by the ratio is, to good approximation,
vortices, anearly linear increase for the next 200 s as the
[HO2] _ kou+co[CO]+koH+cm[CH4]+kon+o3[Oa]
descending vortices and oscillating vortex rings stretch
[OH] /_o,+_o[NO] + k.o_+o_[O._]
the plume volume both vertically and horizontally, and (11)
a slower rate of increase as the vortices dissolve and the
It is this prediction which is sometimes greatly exceeded
Brunt-Viiisii£i oscillations take over and slowly subside
by the observations.
(Figure 4).
The Oa evolution is more interesting, and we might 102 , ,_,,r_
expect more subtle interplay between the chemistry and
dynamics for this species since both the NO photolysis
and NO + Oa reaction (for early plume NO concentra-
tions} occur with characteristic timescales of order 100 10
s, a timescale which is also of importance for the wake
0
dynamics as seen in Figure 1. The destruction of O:_ by
NO within the plume is larger than the production via o_
NO photolysis for the first _170 s (Figure 4) and re- _o o
versed afterward so that an Oa deficit forms but is later
replaced by an O3 surplus, with the age of the crossover
point strongly influenced by the plume dynamics. The
magnitudes above or below background are all small,
10-1
however. At the given NO concentrations, equation (1)
has difficulty competing with the level of plume dilution
continually mixing in fresh O._ from the air outside the
plume, ff either the NO concentration had been an or-
der of magnitude larger, or the plume dilution rates that 10 -2 i
10 -1 10 0 101 10 2
much smaller, the chemistry and dilution rates would
iNO] (ppbv)
have been comparable and the interaction between the
two would have been more complex. An even larger
Figure 5. Apparent [IIO2]/[OII] ratio deduced from
change would make the chemistry fast comparcKi to the
simulation data using 210 m sample lengths, versus the
mixing, and a much stronger anticorrelation between
equilibrium expectation (thick line). Small points are
NO and O:_ would have developed(as seen in the works
,_ampled from wake plume._ of ages 6 and 10 s; open
by Schumann [1989] and Sykes et al. [1992]).
circles for plume at 50 s.
3.3. HO_ Chemistry
Figures 5 and 6 show our simulated [HO2]/[OH] ratio
The effects of the three-dimensional wake dynamics for sample measurements. The format is msin Figure. 2
are much more dramatic for the OH and HO2 chemistry, of Tan el al. [1998] (except for the log scale and sorting
and can explain a puzzle found in the in situ observa- lhe data by wake plume age), with the data sampled
tions of Tan et aL [1998]. hi a series of observations in analogous fashion. The time resolution for the mea-
during SUCCESS. OH, HO2, and NO concentrations surements was 1 s, which at the average flight speed
were measured within the wake plume of a B757 for of 210 m s 1 of the measuring aircraft means an av-
wake ages from about 10 to 100 s. The measuring DC- erage over 210 m for each data sample. Accordingly,
the simulated measurements in Figures 5 and 6 are 210
8 also sampled its own wake at much later ages (about
1200 s). As expected (and ms we find here), the mea- m averages sampled along lines parallel with the flight
sured Oil levels sharply rose upon entering the plume, track at many positions within the simulated wake, at
while the HO_ levels sharply fell (of. their Figure I). ages as noted. As in the ob_rvations, the analogous
The measured ratio of HO2/Ott concentrations as a [1102]/[O1t] mea.surement from the simulation shows
function of NO, however, was about 20-50 times larger values ranging up to 50 times greater than the local
equilibrium predictions (thick line).
than expected (of. their Figure 2). As the anthers
argued, within the plume where the NO levels are high In our simulated chemistry there axe two main effects